On the other side,
the convergence of infinite-series solutions comes
from ratio tests for successive terms of the series
[1]}, [2]}.
In general the three-term relations (REF ) present two linearly
independent solutions [3]}, [4]} and, consequently, two ratios for \(b_{n+1}/b_n\)  but
we have to choose the so-called minimal solution in order to assure the convergence
the continued fraction (REF ).
In fact, if
\(\lim _{n\rightarrow \infty }\left({b_{n+1}}/{b_n}\right)=t_{1}, \qquad \lim _{n\rightarrow \infty }\left({b_{n+1}}/{b_n}\right)=t_{2},\qquad t_1\ne t_2,\) 
